Finite Temperature Phase Diagram of a Two-Component Fermi Gas with Density Imbalance

TL;DR

This paper maps the finite temperature phase diagram of a two-component Fermi gas with density imbalance, revealing stability regions for homogeneous, inhomogeneous, and phase-separated superfluid phases through analytical and numerical methods.

Contribution

It provides a detailed phase diagram considering fixed number densities, highlighting new stable phases and transition behaviors not seen in chemical potential-based analyses.

Findings

Homogeneous superfluid stable at high temperature and low imbalance

LOFF phase persists at low temperature and high imbalance

Phase separation occurs between these regimes

Abstract

We investigated possible superfluid phases at finite temperature in a two-component Fermi gas with density imbalance. In the frame of a general four-fermion interaction theory, we solved in the BCS region the gap equations for the pairing gap and pairing momentum under the restriction of fixed number densities, and analyzed the stability of different phases by calculating the superfluid density and number susceptibilities. The homogeneous superfluid is stable only at high temperature and low number asymmetry, the inhomogeneous LOFF survives at low temperature and high number asymmetry, and in between them there exists another possible inhomogeneous phase, that of phase separation. The critical temperatures and the orders of the phase transitions among the superfluid phases and normal phase are calculated analytically and numerically. The phase diagram we obtained in the temperature and number asymmetry plane is quite different from the one in temperature and chemical potential difference plane for a system with fixed chemical potentials.